The offering or bidding strategy of an agent operating in a day-ahead electricity
market may be optimized by modeling the competitive behavior of its competitors. This can be
done using residual demand curves. For every auction, the residual demand is defined as the
clearing price of the market expressed as a function of the amount of energy the agent is able
to buy or sell. Forecasting residual demand curves is the first and essential step in the design of
optimal bidding strategies.
Residual demand curves can be considered as a functional time series defined as the
realization of a stochastic process where each observation is a continuous function defined on
a finite interval. In order to forecast these curves, a functional Hilbertian ARMAX model is
presented in this paper using functional integral operators in the L2 space. The kernels of the
operators are modeled as linear combinations of sigmoid functions, where the parameters of
each sigmoid are estimated using a Quasi-Newton algorithm which minimizes the sum of
squared functional errors.
This functional model allows forecasting the time series of hourly residual demand curves
taking into account time dependencies, seasonality as well as exogenous variables. An
empirical study is presented for the hourly residual demand curves of the Spanish day?ahead
electricity market.